Conductance of

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Conductance of d-wave SC/normal metal/d-wave
SC junctions
Dmitry Pesin, Anton Andreev, and Boris
Spivak University of Washington
APS March Meeting, New Orleans, March, 10th
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Problem setup
Current through a weak link
(Josephson relation)
- Josephson current
- voltage and phase difference across the junction
Dissipative part of the current is related to the
entropy production
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D-wave symmetry of SC order parameter
Clean d-wave superconductor
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Qualitative picture of the dissipation mechanism

• In adiabatic approximation quasiparticles move
  with levels.
• Thus a nonequilibrium distribution function is
  created

Further details depend on the symmetry of the
order parameter
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DND
In the SNS case the conductance is determined by
the inelastic relaxation time in the normal part
of the junction.
A. D. Zaikin, 1983 S. V. Lempitskii, 1983 F.
Zhou, B. Spivak, 1997 F. Zhou, P. Charlat, B.
Spivak, and B. Pannetier, 1998 K. W. Lehnert et
al., 1999 N. B. Kopnin and J. Voutilainen,
2007.
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DoS in the normal part Usadel Equations
Boundary conditions are different ( )
(Y. Tanaka et al.,2004)
These equations enable one to obtain the DoS in
the N-piece
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Diffusion coefficient and DoS
In a uniform d-wave SC we have
(Born limit)
These expressions are closely related to those
appearing in the theory of thermal conductivity
of unconventional superconductors, P. A. Lee,
1993 A. C. Durst and P. A. Lee, 2000.
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Results

• Periodic function of Á with a period 2¼
• Determined by inelastic relaxation in the leads

For a specific model with
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Conclusions
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1 A. D. Zaikin, Sov. Phys. JETP 57, 910 (1983)
2 S. V. Lempitskii, Sov. Phys. JETP 58, 625
(1983) 3 F. Zhou, B. Spivak, JETP Letters 65,
369 (1997) 4 F. Zhou, P. Charlat, B. Spivak,
and B. Pannetier, J. Low Temp. Phys. 110, 841
(1998) 5 K. W. Lehnert et al., Phys. Rev.
Lett. 82, 1265 (1999) 6 N. B. Kopnin and J.
Voutilainen, Phys. Rev. B 75, 174509 (2007)
1 Y. Tanaka, Yu. V. Nazarov, A. A. Golubov, and
S. Kashiwaya, Phys. Rev. B 69, 144519 (2004)
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1) The diffusive form of the equation is valid in
both normal metal and d-wave SC (at scales gtgt
)
2) Simplification at low T relaxation happens in
the leads, and the generation term can be
substituted with , where